Abstract : The generalized algebraic eigenvalue problem (A - lambda B)x = O arises in the use of the variation method in quantum mechanics. If, within the limitations of the computer word-length, the basis set used to expand the trial wave function is linearly dependent, the matrix B becomes singular. Three different algorithms designed to deal with this difficulty have been investigated, paying special attention to the problem of identifying which members of the basis set are effectively linearly dependent. The advantages and limitations of each method are discussed. (Author)